By the discrete nature of the spin labels defining a spin network basis, the Wheeler-de Witt equation can be represented by a recursion relation of the \(\lbrace 6j\rbrace \) -symbols.
It was proposed in [1]} a spin 1 Hamiltonian (denoted with a superscript \((1)\) ) by projecting the rotation matrix \(R(g_6 g_1 g_2^{-1})\)  onto the fluxes \(\vec{X}_2\)  and \(\vec{X}_6\)  associated to the node where links \(l_2\)  and \(l_6\)  meet,
\(H_{126}^{(1)}=\vec{X}_6 \cdot \left( \mathbb {I}- \text{Ad}(g_6 g_1 g_2^{-1}) \right)\, \vec{X}_2= \vec{X}_6 \cdot \vec{X}_2 - \vec{X}_6 \cdot \text{Ad}(g_1) \,\vec{X}\,.\) 
